http://millionmilesecrets.com/2012/0...vel/#more-8811 series will be helpful. You can call AA and ask about available dates, or search for available seats on various partner airlines using sites other than AA.com; and call in with those dates and flights.
Also, especially if this is in the second half of December and competing for seats with all the Christmas vacation travel, you may want to sign up for a subscription like Expert Flyer to catch seats when they become available.